curve #2906

y² + xy + y = x³ + x² + 55758032391919233690009685x + 1408101440645734666872928942592898134297

a-invariants: [1, 1, 1, 55758032391919233690009685, 1408101440645734666872928942592898134297]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/4ℤ
conductor (N): 23959330209511704615223770
discriminant (Δ): -867642217212625083846002768955713227450543902249209956662139865103797360400000000
Faltings height: 14.2104
naive height: 193.8093
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 23, 31, 41, 43, 97, 193, 241, 2087, 2713
regulator: 56596369.66823016230298848545642336087228040168738221
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:27:48 UTC
last updated: 2026-09-26 20:27:48 UTC

Witness: 7 independent points log in to add more points →

(4698540183107, -42116615275164168154)
(33716514285132881107/998001, 203963650828708484509742960954/997002999)
(-3238133643109, -34548457088047029466)
(9355813250315323/4489, -11777333331094773248673502/300763)
(16088796947707, 80434787492716063646)
(10748450432707, 57001517630502058646)
(-892504265425088033/128881, 1215262019440810506848661934/46268279)

Commentary

2-isogenous image of D-z2z4old678-054, rational kernel x=4782017598099. Source: https://dujella.github.io/tors/z2z4old678.html. Independent witness points transported by the degree-2 isogeny.

last edited by Natanael Wildner Fraga at 2026-09-26 20:27:48 UTC · history